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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 303450.hg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.hg1 | 303450hg2 | \([1, 0, 0, -331778, -435223548]\) | \(-6693187811305/131714173248\) | \(-79481498626288852800\) | \([]\) | \(11197440\) | \(2.4995\) | |
303450.hg2 | 303450hg1 | \([1, 0, 0, 36697, 15716157]\) | \(9056932295/181997172\) | \(-109824232423871700\) | \([]\) | \(3732480\) | \(1.9502\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.hg have rank \(0\).
Complex multiplication
The elliptic curves in class 303450.hg do not have complex multiplication.Modular form 303450.2.a.hg
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.